WASHINGTON — The struggle in Washington over whether to renew expired jobless benefits for the long-term unemployed is as much about providing aid to 1.3 million out-of-work Americans as it is about drawing the first political line of an election year.

Tuesday’s unexpected vote in the Senate removing one obstacle to a three-month extension of aid attracted the support of six Republicans, illustrating the real-life and political pressures on some GOP lawmakers, including those from states with unemployment above the national average.

Still, the legislation’s outcome is uncertain as Democrats, backed by the White House, and Republicans remain sharply divided over whether the cost of the $6.4 billion program extension should be added to the deficit or paid for with spending cuts. Senate Majority Leader Harry Reid, D-Nev., and White House officials indicated they would be receptive to cuts to offset a yearlong renewal of the program, only if Republicans would first agree to restore the benefits for three months without conditions.

The debate fits neatly into a White House strategy to focus much of this year on longstanding economic disparities and draw Republicans into a midterm fight that Democrats believe they win with the public. Income inequality and the lack of upward mobility will be a central theme of Obama’s State of the Union address later this month — a focus White House officials call Obama’s “driving motivation.”

It could be a tricky emphasis. Even as Obama calls attention to what he perceives as structural economic flaws that have created a chasm between haves and have-nots, he is also trying to emphasize the economy’s recovery from the Great Recession. At the same time, unemployment remains high at 7 percent and the total number of long-term unemployed is 4.1 million, a figure underscored by his call for a renewal of the emergency jobless benefits.

Speaking at the White House on Tuesday, Obama said the nation’s economy is getting stronger, but he conceded that “the recovery in a big country like the United States is going to be somewhat uneven.”

What’s more, the White House was observing the 50th anniversary of President Lyndon Johnson’s War on Poverty with an economic report Wednesday that hails government anti-poverty programs but also blames the lack of progress in reducing poverty since the 1980s on rising inequality.

“As every American knows, our work is far from over,” Obama said in a statement marking the anniversary. “In the richest nation on Earth, far too many children are still born into poverty, far too few have a fair shot to escape it, and Americans of all races and backgrounds experience wages and incomes that aren’t rising, making it harder to share in the opportunities a growing economy provides.”

Eager to sustain attention on the economy, Democrats are expected to follow the debate over jobless benefits with a proposal to increase the minimum wage. The strategy matches a script laid out by Obama’s pollster in November that stressed that the economy remained an overriding voter priority. At the time, the troubled rollout of Obama’s health care law was dominating the news, but pollster Joel Benenson argued that it was “imperative that we return to the core issues that animate voters’ lives: a desire for financial security.” The White House distributed the memo to congressional Democrats.

On Tuesday, Senate Minority Leader Mitch McConnell, R-Ky., pounced on Obama and the Democrats and argued that they were complaining about the hardships facing jobless workers “as if somehow there’s no responsibility for that with either the majority in the Senate or the administration.”

While some conservatives have argued that jobless benefits stifle the motivation of unemployed people to look for work, most Republicans cast their objections as an issue of fiscal responsibility, making a case that the benefits should be paid for and accusing Obama of not being responsive to their jobs proposals.

Reid argued that after a series of belt-tightening measures, there are few places to trim the budget. “If they come with something that’s serious, I’ll talk to them,” he said. “But right now, everyone should understand, the low-hanging fruit is gone.”

The three-month measure before the Senate would restore benefits averaging $256 weekly to an estimated 1.3 million long-term jobless who were cut off when the program expired Dec. 28. The federal coverage generally lasts from 14 to 47 weeks, depending on the level of unemployment within individual states. Without action by Congress, hundreds of thousands more will feel the impact in the months ahead as their state-funded benefits expire, typically after 26 weeks.

The six Republicans who voted to overcome a filibuster were Dean Heller of Nevada, Kelly Ayotte of New Hampshire, Dan Coats of Indiana, Susan Collins of Maine, Lisa Murkowski of Alaska and Rob Portman of Ohio.

Heller, Coats and Portman represent states with unemployment above the national average of 7 percent.

Even if Democrats and the White House succeed in pushing a bill through the Senate, it still faces a challenge in the Republican-controlled House, where Speaker John Boehner made clear he would not rubber-stamp a Senate-passed bill. He said he has previously informed the White House that any measure to renew unemployment benefits “should not only be paid for but include something to help put people back to work. To date, the president has offered no such plan.”

Democrats were quick to apply political pressure. At the White House, Obama surrounded himself with unemployed Americans and was introduced by Katherine Hackett, an unemployed single mother from Connecticut whose two sons are serving in the military. He said the complaint that aid to the unemployed dampens their job-seeking “really sells the American people short.”

“These aren’t folks who are just sitting back, waiting for things to happen,” he said. “They’re out there actively looking for work.”

Meanwhile, some Democrats, including Sens. Chris Coons of Delaware and Jeanne Shaheen of New Hampshire, used the debate as a fundraising pitch in emails seeking donations from contributors. “We have to continue putting pressure on Republicans in the House and Senate to get these life-saving benefits renewed,” Shaheen said in an email to supporters.

On Wednesday, Ayotte, Portman and four other Republicans senators planned to propose an amendment that would pay for the three-month benefit renewal and restore full cost-of-living increases for military retirees by preventing immigrants in the United States illegally from claiming a child tax credit.